In this 1958 book, Professor Hanson turns to an equally important but comparatively neglected subject, the philosophical aspects of research and discovery.

Conflicting accounts of the role of mathematics in our physical theories can be traced to two principles. Mathematics appears to be both (1) theoretically indispensable, as we have no acceptable non-mathematical versions of our theories, and (2) metaphysically dispensable, as mathematical entities, if they existed, would lack a relevant causal role in the physical world. I offer a new account of a role for mathematics in the physical sciences that emphasizes the epistemic benefits of having mathematics around when we do (...) science. This account successfully reconciles theoretical indispensability and metaphysical dispensability and has important consequences for both advocates and critics of indispensability arguments for platonism about mathematics. (shrink)

From Kant’s first published work to recent articles in the physics literature, philosophers and physicists have long sought an answer to the question, why does space have three dimensions. In this paper, I will flesh out Kant’s claim with a brief detour through Gauss’ law. I then describe Büchel’s version of the common argument that stable orbits are possible only if space is three-dimensional. After examining objections by Russell and van Fraassen, I develop three original criticisms of my own. These (...) criticisms are relevant to both historical and contemporary proofs of the dimensionality of space (in particular, a recent one by Burgbacher, F. Lämmerzahl, C., and Macias). In general I argue that modern “proofs” of the dimensionality of space have gone off track. (shrink)

Certain scientific explanations of physical facts have recently been characterized as distinctively mathematical –that is, as mathematical in a different way from ordinary explanations that employ mathematics. This article identifies what it is that makes some scientific explanations distinctively mathematical and how such explanations work. These explanations are non-causal, but this does not mean that they fail to cite the explanandum’s causes, that they abstract away from detailed causal histories, or that they cite no natural laws. Rather, in these explanations, (...) the facts doing the explaining are modally stronger than ordinary causal laws or are understood in the why question’s context to be constitutive of the physical arrangement at issue. A distinctively mathematical explanation works by showing the explanandum to be more necessary than ordinary causal laws could render it. Distinctively mathematical explanations thus supply a kind of understanding that causal explanations cannot. 1 Introduction2 Some Distinctively Mathematical Scientific Explanations3 Are Distinctively Mathematical Explanations Set Apart by their Failure to Cite Causes? 4 Distinctively Mathematical Explanations do not Exploit Causal Powers5 How these Distinctively Mathematical Explanations Work6 Conclusion. (shrink)

As Aristotle stated, scientific explanation is based on deductive argument--yet, Wesley C. Salmon points out, not all deductive arguments are qualified explanations. The validity of the explanation must itself be examined. _Four Decades of Scientific Explanation_ provides a comprehensive account of the developments in scientific explanation that transpired in the last four decades of the twentieth century. It continues to stand as the most comprehensive treatment of the writings on the subject during these years. Building on the historic 1948 essay (...) by Carl G. Hempel and Paul Oppenheim, "Studies in the Logic of Explanation,” which introduced the deductive-nomological model on which most work on scientific explanation was based for the following four decades, Salmon goes beyond this model's inherent basis of describing empirical knowledge to tells us “not only _what,_ but also _why_.” Salmon examines the predominant models in chronological order and describes their development, refinement, and criticism or rejection. _Four Decades of Scientific Explanation_ underscores the need for a consensus of approach and ongoing evaluations of methodology in scientific explanation, with the goal of providing a better understanding of natural phenomena. (shrink)

Many of the things that we try to explain, in both our common sense and our scientific engagement with the world, are capable of being explained more or less finely: that is, with greater or lesser attention to the detail of the producing mechanism. A natural assumption, pervasive if not always explicit, is that other things being equal, the more finegrained an explanation, the better. Thus, Jon Elster, who also thinks there are instrumental reasons for wanting a more fine-grained explanation, (...) assumes that in any case the mere fact of getting nearer the detail of production makes such an explanation intrinsically superior: “a more detailed explanation is also an end in itself”. Michael Taylor agrees: “A good explanation should be, amongst other things, as fine-grained as possible.”. (shrink)

Philosophers have proposed many alleged examples of non-causal explana- tions of particular events. I discuss several well-known examples and argue that they fail to be non-causal.

A conservation law in physics can be either a constraint on the kinds of interaction there could be or a coincidence of the kinds of interactions there actually are. This is an important, unjustly neglected distinction. Only if a conservation law constrains the possible kinds of interaction can a derivation from it constitute a scientific explanation despite failing to describe the causal/mechanical details behind the result derived. This conception of the relation between “bottom-up” scientific explanations and one kind of “top-down” (...) scientific explanation is motivated by several examples from classical and modern physics. (shrink)

Philosophers of science take it as a datum that Mayor John's having syphilis explains why he, rather than certain nonsyphilitics, had paresis. Using a new hypothetical example, the case of the two dams, it is argued that three independent considerations invalidate these philosophers' starting point.